Convert the complex no. In polar form : 1-i
rcosΘ =1
rsinΘ=-1
r=√a2+b2
r=√(1)2+(-1)2
r=√2
TanΘ=b/a
=1/-1
=-1
After all this what i have to do to find out value of Θ?
Please help me..
For polar form,
=r(cosΘ+isinΘ)
You are correct so far, r = √2
all you need is Ø, and you almost got it
tanØ = -1
we know that tan π/4 = +1, (tan 45° = 1)
and we also know that 1 - i would form an angle in quadrant IV
so Ø must be 2π - π/4 = 7π/4
so 1 - i = √2cos 7π/4 + √2sin 7π/4
or √2(cos 7π/4 + sin 7π/4)
Here is an excellent clip by Sal Khan
https://www.khanacademy.org/math/precalculus/imaginary-and-complex-numbers/polar-form-of-complex-numbers/v/polar-form-complex-number
Thanks for helping m
Thanks for helping me
To find the value of Θ in the polar form of a complex number, you can use the equation:
TanΘ = b/a
In this case, b = -1 and a = 1. So,
TanΘ = -1/1
Θ = Tan^(-1)(-1/1)
To find the value of Θ, you can take the inverse tangent (also known as arctan) of -1/1. On most calculators, you can find the arctan function by pressing the "tan" button, followed by the "-1" or "inv" button.
After finding the value of Θ, you can write the complex number 1 - i in polar form as r(cosΘ + isinΘ), where r is the magnitude and Θ is the angle. The magnitude, in this case, is √2 as you calculated earlier, and Θ is the value you found using the arctan function.